The latent heat of melting is the amount of energy needed to convert a solid substance at its melting temper-
ature to a liquid at the same temperature. For typical volcanic rocks, the latent heat of melting is around
5×105 J/kg, which means it takes 5×105 J to turn 1 kg of volcanic rock from solid at its melting temperature
to liquid at the same temperature. Assuming that providing the latent heat of melting is the only important
time-limiting step in turning Io’s rocks to liquid, how much time does it take to completely melt all of Io’s
crust? This is the resurfacing time for Io.
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It seems to me that you need to know the thickness of the crust and how fast heat is added to it. This information is not provided.
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